Intersection-union test

For a null hypothesis that is a union $H_0={\bigcup }_{i\in I}{H}_i$, an intersection-union test rejects $H_0$ only when every component $H_i$ is rejected. If each component test has level $\alpha$, then under any point of $H_0$ at least one component null is true, so the combined test also has level at most $\alpha$.